- #1

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a= [1 1 1]

b= [2 L 0]

c= [L 2 3]

How do I calculate the L in order to make these vecotrs linearly dependent?

How does ß depend from L if v= [ß 0 -1] and v is in span(a b c)?

Thank you!

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- Thread starter gotmejerry
- Start date

- #1

- 9

- 0

a= [1 1 1]

b= [2 L 0]

c= [L 2 3]

How do I calculate the L in order to make these vecotrs linearly dependent?

How does ß depend from L if v= [ß 0 -1] and v is in span(a b c)?

Thank you!

- #2

HallsofIvy

Science Advisor

Homework Helper

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For the second question, are we to assume that L is one of those values? Otherwise, the span of a, b, and c is all of R

- #3

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I wrote 3 equations:

α + 2β + Lγ = 0

α + Lβ + 2γ = 0

α + + 3γ = 0

And i got, L can be 1 or 2. Then I checked it and for these Ls the vectors are dependents. But how do I know that there aren't more Ls.

For the second question. Yes L is from those values.

- #4

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- 0

means? Use the definition of "linearly dependent" You will get a cubic equation for L but, fortunately, there's 1 obvious root.

For the second question, are we to assume that L is one of those values? Otherwise, the span of a, b, and c is all of R^{3}and [itex]\beta[/itex] can be anything.

But I maybe got the definition wrong.

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